Question

In which direction must the graph of f(x) = 7x be shifted to produce the graph of g(x) = 7x - 3?

Answer 1

Answer:

"the graph of f(x) needs to be shifted vertically 3 units down to produce the graph of g(x)"

Step-by-step explanation:

If we have a function of the form:

f(x) = ax

We can say:

• f(x) = ax + b  is the parent shifted b units up
• f(x) = ax - b is the parent shifted b units down
• f(x) = a(x-b) is the parent shifted b units right
• f(x) = a(x+b) is the parent shifted b units left

These are the function transformation rules (both vertical and horizontal shift).

Looking at the transformed function ,  g(x) = 7x - 3, this goes with the rule "transformation vertically 3 units down" from the rules above.

So the graph of f(x) needs to be shifted vertically 3 units down to produce the graph of g(x).